The response of epitaxial CoFe2O4 thin films to biaxial compressive stress imposed by MgAl2O4 and SrTiO3 single crystalline substrates is studied using X-ray diffraction and Raman spectroscopy. It is found that the Poisson ratio ν signals a non-auxetic behavior and depends on the substrate used. The Raman modes show an increase in frequency when increasing compressive strain by reducing film thickness; this is due to the shrinking of the unit cell volume. Such behavior is in qualitative agreement with recent ab initio calculations, although the measured values are significantly smaller than predictions. In contrast, the measured Poisson ratio is found to be in good agreement with expectations based on general arguments of atomic packing density. Possible guidelines for searching auxetic response in materials with spinel structure are discussed.